Posterior Distribution of Percentiles: Bayes' Theorem for Sampling From a Population

Abstract

A Bayesian approach to inference about the percentiles and other characteristics of a finite population is proposed. The approach does not depend upon, though it need not exclude, the use of parametric models.Some related questions concerning the existence of exchangeable distributions are considered. It is shown that there are no countably additive exchangeable distributions on the space of observations which give ties probability 0 and for which a next observation is conditionally equally likely to fall in any of the open intervals between successive order statistics of a given sample.